Finite Group Databasebeta

← C19×#10207 #18016166

Subgroups — C19×#10207 #18016166

Order 4864.

474 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3249C211yesmaximal, characteristic
2C19×#3229C211yesmaximal, characteristic
3C19×#3139C211yesmaximal, characteristic
4C19×#1988C211yesmaximal, characteristic
5C19×#1986C211yesmaximal, characteristic
6C19×#1503C211yesmaximal, characteristic
7C19×#1283C211yesmaximal, characteristic
8C19×#533C2211yescharacteristic
9C19×#533C2211yescharacteristic
10C2×C19×C4⋊Q8C2211yescharacteristic
11C19×#498—21no—
12C19×#491—22no—
13C19×#487—21no—
14C19×#487—21no—
15C19×#487—21no—
16C19×#483—22no—
17C19×#477—21no—
18C19×#477—21no—
19C19×#475—22no—
20C19×#467—22no—
21C19×#462—21no—
22C19×#462—21no—
23C19×#431C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C19×#419—22no—
26C4×M16×C19C2211yescharacteristic
27C4×C4⋊C4×C19C2211yescharacteristic
28C19×#340—22no—
29C19×#339—22no—
30C19×#328—22no—
31C22×Q8×C19—21no—
32C2×Q16×C19—22no—
33C2×M16×C19D412yes—
34C22×C8×C19D412yes—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C19×C4⋊Q8D411yescharacteristic
39C19×C4⋊Q8D411yescharacteristic
40C19×C4⋊Q8D412yes—
41C19×C4⋊Q8D411yescharacteristic
42C19×C4⋊Q8D411yescharacteristic
43C19×#125—21no—
44C19×#125—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8—21no—
48C19×C22⋊Q8—21no—
49C4×Q8×C19—21no—
50C4×Q8×C19—21no—
51C4×Q8×C19—21no—
52C4×Q8×C19—21no—
53C19×#117—21no—
54C19×#117—21no—
55C2×C4⋊C4×C19—21no—
56C2×C4⋊C4×C19—21no—
57C2×C4⋊C4×C19—21no—
58C2×C42×C19—21no—
59C2×C42×C19C2311yescharacteristic
60C19×#107—22no—
61C19×#106—24no—
62C19×C4⋊C8—21no—
63C19×C4⋊C8—21no—
64C19×C4⋊C8—21no—
65C19×#103—24no—
66C19×#103—24no—
67C19×#103—22no—
68C19×#103—22no—
69C19×#103—24no—
70C19×C22⋊C8D412yes—
71C19×#97—21no—
72C4×C8×C19—21no—
73C4×C8×C19—21no—
74C19×#95—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19—22no—
79C2×Q8×C19—21no—
80C2×Q8×C19—41no—
81C2×Q8×C19—42no—
82C2×Q8×C19—42no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88Q16×C19—82no—
89M16×C19—22no—
90M16×C19—22no—
91C2×C8×C19—22no—
92C2×C8×C19—22no—
93C2×C8×C19—22no—
94C2×C8×C19—42no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19—41no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C22⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C42×C19—41no—
116C42×C19—41no—
117C42×C19—42no—
118C42×C19C2×D411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19#4111yescharacteristic
122#10207C1911yesmaximal, characteristic, direct product factor, Sylow
123C23×C19#12711yescharacteristic
124Q8×C19—42no—
125Q8×C19—44no—
126Q8×C19—41no—
127Q8×C19—41no—
128Q8×C19—41no—
129Q8×C19—41no—
130Q8×C19—81no—
131Q8×C19—82no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19—81no—
142C2×C4×C19—81no—
143C2×C4×C19—81no—
144C2×C4×C19—81no—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12011yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#13512yes—
152C2×C4×C19#13712yes—
153C8×C19—42no—
154C8×C19—42no—
155C8×C19—42no—
156#3249C2×C1911yescharacteristic
157#3229C2×C1911yescharacteristic
158#3139C2×C1911yescharacteristic
159#1988C2×C1911yescharacteristic
160#1986C2×C1911yescharacteristic
161#1503C2×C1911yescharacteristic
162#1283C2×C1911yescharacteristic
163C22×C19—21no—
164C22×C19—21no—
165C22×C19#39211yescharacteristic
166C22×C19#49511yescharacteristic
167C22×C19#49711yescharacteristic
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—82no—
172C4×C19—81no—
173C4×C19—81no—
174C4×C19—81no—
175C4×C19—81no—
176C4×C19—82no—
177C4×C19#45212yes—
178C4×C19#45511yescharacteristic
179C4×C19#45611yescharacteristic
180C4×C19#46412yes—
181#533C22×C1911yescharacteristic
182#533C22×C1911yescharacteristic
183C2×C4⋊Q8C22×C1911yescharacteristic
184#498—21no—
185#491—22no—
186#487—21no—
187#487—21no—
188#487—21no—
189#483—22no—
190#477—21no—
191#477—21no—
192#475—22no—
193#467—22no—
194#462—21no—
195#462—21no—
196#431C22×C1911yescharacteristic
197C2×C4⋊C8C22×C1911yescharacteristic
198#419—22no—
199C4×M16C22×C1911yescharacteristic
200C4×C4⋊C4C22×C1911yescharacteristic
201#340—22no—
202#339—22no—
203#328—22no—
204C2×C19—21no—
205C2×C19—21no—
206C2×C19#200711yescharacteristic
207C2×C19#200911yescharacteristic
208C2×C19#201511yescharacteristic
209C22×Q8—21no—
210C2×Q16—22no—
211C2×M16D4×C1912yes—
212C22×C8D4×C1912yes—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8D4×C1912yes—
217C4⋊Q8D4×C1911yescharacteristic
218C4⋊Q8D4×C1911yescharacteristic
219C4⋊Q8D4×C1911yescharacteristic
220C4⋊Q8D4×C1911yescharacteristic
221#125—21no—
222#125—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231#117—21no—
232#117—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C42—21no—
237C2×C42C23×C1911yescharacteristic
238#107—22no—
239#106—24no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243#103—24no—
244#103—24no—
245#103—22no—
246#103—22no—
247#103—24no—
248C22⋊C8D4×C1912yes—
249#97—21no—
250C4×C8—21no—
251C4×C8—21no—
252#95—21no—
253C19#1020711yescharacteristic, direct product factor, Sylow
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—41no—
260C2×Q8—42no—
261C2×Q8—42no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C1911yescharacteristic
265C22×C4C2×D4×C1911yescharacteristic
266C22×C4C2×D4×C1911yescharacteristic
267Q16—82no—
268M16—22no—
269M16—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—42no—
274C4⋊C4—22no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—41no—
295C42—41no—
296C42—42no—
297C42C2×D4×C1911yescharacteristic
298C42C2×D4×C1911yescharacteristic
299C42C2×D4×C1911yescharacteristic
300C42#41×C1911yescharacteristic
301C23C19×#12711yescharacteristic
302Q8—42no—
303Q8—44no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308Q8—81no—
309Q8—82no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C19×#12011yescharacteristic
324C2×C4C19×#12011yescharacteristic
325C2×C4C19×#12011yescharacteristic
326C2×C4C19×#12111yescharacteristic
327C2×C4C19×#12111yescharacteristic
328C2×C4C19×#12111yescharacteristic
329C2×C4C19×#13512yes—
330C2×C4C19×#13712yes—
331C8—42no—
332C8—42no—
333C8—42no—
334C22—21no—
335C22—21no—
336C22C19×#39211yescharacteristic
337C22C19×#49511yescharacteristic
338C22C19×#49711yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—82no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—82no—
348C4C19×#45212yes—
349C4C19×#45511yescharacteristic
350C4C19×#45611yescharacteristic
351C4C19×#46412yes—
352C2—21no—
353C2—21no—
354C2C19×#200711yescharacteristic
355C2C19×#200911yescharacteristic
356C2C19×#201511yescharacteristic
subgroupG/H
center, socleC22×C19#392
commutator, Frattini, cosocleC2×C42C23×C19
prime radicalC23×C19#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
122. #10207C19direct (N × H)
253. C19#10207direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C19×#32492
C19×#32292
C19×#31392
C19×#19882
C19×#19862
C19×#15032
C19×#12832
#1020719